The Stick-Breaking Construction of the Beta Process as a Poisson Process
Statistics Theory
2012-04-20 v2 Probability
Machine Learning
Statistics Theory
Abstract
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.
Keywords
Cite
@article{arxiv.1109.0343,
title = {The Stick-Breaking Construction of the Beta Process as a Poisson Process},
author = {John Paisley and David Blei and Michael I. Jordan},
journal= {arXiv preprint arXiv:1109.0343},
year = {2012}
}
Comments
We've updated with the conference version of the paper. Please note that the title has changed